Critical exponent of infinite balanced words via the Pell number system
Formal Languages and Automata Theory
2019-11-15 v3 Discrete Mathematics
Combinatorics
Abstract
In a recent paper of Rampersad et al., the authors conjectured that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is . We prove this result, using a formulation of first-order logic, the Pell number system, and a machine computation based on finite-state automata.
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Cite
@article{arxiv.1902.00503,
title = {Critical exponent of infinite balanced words via the Pell number system},
author = {Aseem Raj Baranwal and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1902.00503},
year = {2019}
}
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14 pages